Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+9y &= 9 \\ 8x+6y &= 6\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $6y = -8x+6$ Divide both sides by $6$ to isolate $y$ $y = {-\dfrac{4}{3}x + 1}$ Substitute this expression for $y$ in the first equation. $-7x+9({-\dfrac{4}{3}x + 1}) = 9$ $-7x - 12x + 9 = 9$ Simplify by combining terms, then solve for $x$ $-19x + 9 = 9$ $-19x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $-7( 0)+9y = 9$ $9y = 9$ $9y = 9$ $y = 1$ The solution is $\enspace x = 0, \enspace y = 1$.